What is the value of h when the function is converted to vertex form? note: vertex form is h(x)=a(x−h)^2+k . h(x)=x^2−8x+14 enter your answer in the box.

h = 4  

Step-by-step explanation:

Step-by-step explanation:

The standard form of a quadratic function is  

y = ax² + bx + c

Your function is

h(x) = x² − 8x + 14

a = 1; b = -8; c = 14

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

Calculate h

h = -(-8)/(2×1)

  =      8/2

 =        4

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

3030 ur welcome

step-by-step explanation: